Scaling behavior of an Anderson impurity close to the Mott-Anderson transition

TL;DR

This paper investigates how Anderson impurity models behave near the Mott-Anderson transition, focusing on the scaling of quasiparticle weight and magnetic moments depending on site energy and transition proximity.

Contribution

It introduces a detailed analysis of the scaling behavior of quasiparticle weight Z near the transition, highlighting the role of site energy in magnetic moment formation.

Findings

Z scales with site energy and transition distance

Impurity site can become a local magnetic moment or remain doubly occupied

Beta function interpretation of the scaling behavior

Abstract

The scaling behavior of Anderson impurity models each of which with a different site energy epsilon_i is examined close to the Mott-Anderson transition. Depending on the impurity energy epsilon_i, in the critical regime the site turns into a local magnetic moment, as indicated by a vanishing quasiparticle weight Z -> 0, or remains nearly doubly occupied or nearly empty, corresponding to Z -> 1. In this paper, we present the scaling behavior of Z as a function of the on-site energy epsilon_i and the distance t to the transition, and interpret our result in terms of an appropriate beta function beta(Z).